Quick passports
We managed to get our passport for bubs in 2 days - but we had to how proof of travel dates to with babies name on for them to rush it through. I think normally they say 10 days, but think that unless they are very busy it is usually back before this. The office is very good and not very busy - think it took us 30 mins to wait and get form in and then about 2 to collect the passport!!
With the passport photo we had ours done in the photo place in Princes Building (same floor as Olivers). They were really good, took a pic of hubby and baby and then just chopped it down to size - they took quite a few before they took one that they thought was good and the passport office said it was fine.
We had only been in HK for just over a year and did not have anybody to sign the form here that had known us for 2 years. They said it was fine for someone who had known us for less time to sign it, we just needed to write this in the "other details" section.
With the birth certificate, the hospital will tell you where to register (in Central it is by Pacific Place) - you need passports, marriage certificate (if you have one) and think maybe birth certificates but not sure. Again it took about half an hour to do and they were really good. A word of warning though - they only process so many births in one day, so when we went to register at 3.30 they had filled there quota and we had to go back the next day!! They usually suggest that you wait 14 days as well, to make sure that the hospital has sent all the documents down.
We took bubs to Singapore at 5 weeks and that was fine and i was chatting to someone the other day who took their baby back to India at 2 weeks.
Hope that helps - searching the British Consulate and Birth registration in Hong kong should help you work everything out.
Good luck
Em x